MATHEMATICS

1)      Suppose that next year the U.S. will be in one of the following economic conditions: Boom, Moderate Growth, Recession, or Depression. The probability that each economic condition will occur, and that a jewelry store will earn profits within that broader economic condition are listed below:

Economics condition Profit probability
Boom 400000 0,4
moderategrowth 300000 0,3
recession 100000 0,2
depression -500000 0,1

2)      The standard deviation of the jewelry store’s profits next year (rounded to the nearest dollar) is ?

3)      The expected profit of the jewelry store during the next year is?

4)      What is the complete set of numbers for which f(x) = x3 + 2x2 – x is concave?

5)      Today you deposited $10,000 in a savings account that pays 6% annual interest, compounded semiannually. In 5 years, how much money will you have in your account (rounded to the nearest dollar)?

6)      Today you put $1000 in the bank. Your bank pays 5% interest, continuously compounded. In 3 years, how much money will you have in the bank (rounded to the nearest dollar)?

7)      Suppose that you draw two cards from a deck. After drawing the first card, you do not put the first card back in the deck. What is the probability (rounded to the nearest ten thousandth) that both cards are diamonds?

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